assassins have high pick rates for 3 reasons: high skill caps(in some cases); they counter mages; they are very mobile and powerful with the assassin fantasy of killing a target before they can react...
just look at the tier list or any data on any site. Assassins and specialists that mimic assassins are HUGELY successful. here is u.gg ; https://u.gg/lol/tier-list/?role=middle&rank=diamond_plus
click on the tier list...notice something? 5 out of the top 10 are assassins, 2 of those are specialists that MIMIC assassins or FORMERLY WERE ASSASSINS , then 2 of the others are ASSASSIN COUNTERS
9 out of 10 of the top 10 picks have to do with assassins
#btw, zhonya's without armor might still get picked, but, do you know what is more likely to happen? either an HP item or an amor item would replace it simply due to mages popping like balloons with only HEALTH in their item lists
is likely or another 
if I had to hazard a guess,
would replace zhonya's unless zhonya's received a substantial increase in AP or a substantial decrease in its cool-down and then
would be used to deal with AD threats, providing a weaker but still better than nothing defense. There's also
just to be able to survive at all
no they're not. saying that AD and AS champions are the strongest is just a biased opinion
I'll list pick rates and win rates
22% pick rate, 51.24% win rate
(although not strictly AD, he does build primarily AD items and then defensive items) 22% pick rate, 49% win rate on a very high skill cap and supposedly high skill floor champion
15.8% pick rate, 52.18% win rate
13.6% pick rate, 50% win rate, 41% BAN RATE
on second thought, maybe ban rates are a better metric...
41%
36%
33%
28.7%
25%
24.8%
22%
20.4%
19.7%
14.8%
then if you go through most of the ban-rates, the highest have either been buffed like crazy , or, get this, COUNTER AD CHAMPIONS OR ASSASSINS OR ARE ASSASSINS THEMSELVES
there's a thing called macro and positioning that really helps to counter that
seriously, you do realize that mages are #2 on the list of priority targets, right? Marksmen/assassins, mages, melee carries, supports, juggernauts, tanks
If anything can hit mages, they will die and even with good positioning, there are plenty of ways for that to happen
pretty much anything that is capable of attacking will kill a mage and most assassins have a near instant kill time or can delay it until after zhonyas